A255407 - OEIS

%I #16 Feb 22 2015 23:29:56

%S 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,23,20,21,22,25,24,19,26,

%T 27,28,29,30,37,32,33,34,35,36,41,38,39,40,43,42,47,44,45,46,53,48,31,

%U 50,51,52,61,54,49,56,57,58,67,60,71,62,63,64,65,66,77,68,69,70,83,72,89,74,75,76,59,78,91,80,81

%N Permutation of natural numbers: a(n) = A255127(A252460(n)).

%C a(n) tells which number in Ludic array A255127 is at the same position where n is in array A083221, the sieve of Eratosthenes. As both arrays have A005843 (even numbers) and A016945 as their two topmost rows, both sequences are among the fixed points of this permutation.

%C Equally: a(n) tells which number in array A255129 is at the same position where n is in the array A083140, as they are the transposes of above two arrays.

%H Antti Karttunen, <a href="/A255407/b255407.txt">Table of n, a(n) for n = 1..8192</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%F a(n) = A255127(A252460(n)).

%F Other identities. For all n >= 1:

%F a(2n) = 2n. [Fixes even numbers.]

%F a(3n) = 3n. [Fixes multiples of three.]

%F a(A008578(n)) = A003309(n). [Maps noncomposites to Ludic numbers.]

%F a(A001248(n)) = A254100(n). [Maps squares of primes to "postludic numbers".]

%F a(A084967(n)) = a(5*A007310(n)) = A007310((5*n)-3) = A255413(n). [Maps A084967 to A255413.]

%F (And similarly between other columns and rows of A083221 and A255127.)

%e A083221(8,1) = 19 and A255127(8,1) = 23, thus a(19) = 23.

%e A083221(9,1) = 23 and A255127(9,1) = 25, thus a(23) = 25.

%e A083221(3,2) = 25 and A255127(3,2) = 19, thus a(25) = 19.

%o (define (A255407 n) (A255127 (A252460 n)))

%Y Cf. A001248, A003309, A007310, A008578, A083221, A084967, A252460, A254100, A255413, A255127.

%Y Inverse: A255408.

%Y Similar permutations: A249818.

%K nonn

%O 1,2

%A _Antti Karttunen_, Feb 22 2015